My Mom's 2011 iMac is having issues loading web pages.

This past week my mother's iMac (2011) began having issues with the internet. She told me that whenever she ties to search for something on the internet, the reload bar in Safari constantly spins and takes forever to load (around 40 seconds).

We are using an Air Port Extreme router (2011 model), and my mom's iMac still has Snow Leopard (Mac OS X [10.6.8]) installed. The other computers in our house (a 2009 HP Touchsmart, a 2011 MacBook Pro, and a 2013 MacBook Pro) have no issue whatsoever. I recently had to restart the AirPort device in June due to issues, but it was fine for the last month up until Sunday, July 20th, 2014. The iMac is connected to the AirPort Wi-Fi network, but it's incredibly slow.

Is this problem happening because she hasn't updated her computer to OS X Mavericks?